First, relax. At 14 you are much, much, much to young to be considering any type of surgery. Further, surgery for vocalists is pretty much contained to removing nodules that develop on the vocal chords from improper technique and abuse.
There are several reasons why you sound "nasily":
The music you listen to - your second sound clip featured you singing a Miley Cyrus song, and naturally, you imitate the people you listen to. Miley has fairly poor vocal technique and sings with a nasily, strident tone. If you want to make beautiful sounds you must listen to beautiful sounds.
You are young - at 14 your voice has just begun to develop out of adolescence and it is a process that will take many years before your voice is fully mature. That's just the way our bodies work. Your voice is very young and you should not push it into places it shouldn't go. If you sing and get tired, take a rest, don't force it.
Lack of training - lessons, knowledge, technique, and guidance from an experienced voice teacher (not a "vocal coach") will set you up for success and many years of beautiful singing.
Too tense / Need more air - tenseness causes restriction of airflow and vocal cord resonance. If your vocal cords can't resonate fully (with a good supply of air!) your tone will suffer.
Vocal training (taking lessons) is something that will be on-going and it will take years and years for your voice to develop. In an age where everyone expects everything to be immediate, if it's worth doing, isn't it worth taking the time to do it right?